Question

How many AND gates are required to realize Y = CD + EF + G

• A. \( \text{2} \)
• B. \( \text{5} \)
• C. \( \text{3} \)
• D. \( \text{4} \)

Hint:

In digital logic, a sum-of-products (SOP) expression like \( \text{Y = AB + CD + E} \) is typically realized using a two-level AND-OR gate network. Each product term (e.g., \( \text{AB} \), \( \text{CD} \)) requires one AND gate. Single literals (e.g., \( \text{E} \)) are usually fed directly to the OR gate and do not require an AND gate. When counting gates, always consider the most minimal and standard implementation unless specified otherwise. If an answer contradicts this, there might be specific context or a flawed question.

Answer 1

The Correct Option is A

To solve this problem, we need to determine the number of AND gates required to realize the given Boolean expression:

Expression: \( Y = CD + EF + G \)

1. Breaking Down the Expression:

The given Boolean expression consists of three terms: \( CD \), \( EF \), and \( G \). Let's examine the number of AND gates needed to implement each part:

• First term: \( CD \) – This term requires 1 AND gate to combine the inputs \( C \) and \( D \).
• Second term: \( EF \) – This term requires 1 AND gate to combine the inputs \( E \) and \( F \).
• Third term: \( G \) – This term is a single input, so no AND gate is needed for this term (it is treated as a direct input).

2. Implementing the OR Operation:

The output of the AND gates for \( CD \) and \( EF \) needs to be ORed together along with \( G \). An OR gate is needed to combine these three terms into the final output \( Y \). The OR gate, however, does not contribute to the number of AND gates, as it is a separate logic gate.

3. Total AND Gates:

Therefore, the number of AND gates required to realize the expression \( Y = CD + EF + G \) is:

• 1 AND gate for \( CD \)
• 1 AND gate for \( EF \)
• No AND gate is needed for \( G \)

Final Answer:

The number of AND gates required is 2.